Simple Linear Regression

Simple linear regression is a model that describes a continuous outcome as a straight-line function of a single predictor, estimating the intercept and slope by ordinary least squares.

단순선형회귀는 연속형 결과변수를 하나의 예측변수에 대한 직선 함수로 나타내고, 최소제곱법으로 절편과 기울기를 추정하는 모형이다.

How do I estimate how much my outcome changes for each one-unit increase in a single predictor?

예측변수 하나가 한 단위 늘 때 결과가 얼마나 변하는지 어떻게 추정하나요?

Simple linear regression fits a straight line relating one predictor to a continuous outcome, and the slope estimates the expected change in the outcome per one-unit change in the predictor. Its inferences rest on a linear relationship and independent, roughly normal residuals with constant variance, which should be checked with residual diagnostics.

When to use Simple Linear Regression

• One continuous or binary predictor and one continuous outcome
• Estimating and testing the slope of a linear relationship
• Predicting an outcome from a single variable

When to use something else

• Several predictors or control variables: use multiple linear regression
• Binary or count outcomes: use binary logistic or Poisson regression

Assumptions and requirements

• Linear relationship between predictor and outcome
• Independent residuals (Durbin-Watson check)
• Constant residual variance (Breusch-Pagan check)
• Approximately normal residuals

What the analysis reports

• Intercept and slope with standard errors, t, p and 95% confidence intervals
• R² and adjusted R²
• Overall F test with p-value
• AIC and BIC
• Residual diagnostics: normality, Breusch-Pagan and Durbin-Watson

How to report it

A simple linear regression showed that [predictor] significantly predicted [outcome], b = [value], 95% CI [[value], [value]], t([df]) = [value], p = [value], and the model explained [value]% of the variance, R² = [value], F(1, [df]) = [value], p = [value].

Related methods

• Multiple Linear Regression
• Pearson Correlation Analysis
• Robust Regression Analysis

Run Simple Linear Regression on Quorant